Problem Solving

BTGmoderatorLU wrote:Source: GMAT Prep

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per students was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

The OA is D

Total number of books borrowed = T = 30*2 = 60;

Total number of books borrowed by 12 students = A = 1*12 = 12;

Total number of books borrowed by 10 students = B = 2*10 = 20;

Thus, the number of students who borrowed at least 3 books = 30 - 2 - 12 - 10 = 6;

Since we need to maximize the number of books any single student can borrow, let's assume that out of the remaining 6 students, barring ONE student, 5 borrowed the minimum number of books, i.e., 3 each.

Thus, the total number of books borrowed by 5 students = C = 3*5 = 15;

Say, the single student borrowed D number of books; thus, we have

T = A + B + C + D

60 = 12 + 20 + 15 + D

=> D = 13

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: GMAT Prep

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per students was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

The OA is D

The average (arithmetic mean) number of book borrowed per student was 2.
Since there are 30 students altogether, the total number of borrowed books = (2)(30) = 60

2 students borrowed 0 books: total of 0 books
12 students borrowed 1 book each: total of 12 books
10 students borrowed 2 books each: total of 20 books
6 students borrowed 3 or more books each: total of 28 books (since the total borrowed books must equal 60)

Now we'll focus on the 6 students who borrowed a total of 28 books.
In order to MAXIMIZE the number of books that one students borrowed, we need to MINIMIZE the number of books that the other 5 students borrowed.
Each student must borrow at least 3 books, so let's say that those 5 students borrowed 3 books each.
This accounts for 15 books, which means the last remaining student borrowed 13 books.

Answer: D

Cheers,
Brent

BTGmoderatorLU wrote:Source: GMAT Prep

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per students was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

The OA is D

Since the average number of books per student was 2, the total number of books borrowed was 2 x 30 = 60 books.

The number of books borrowed by the students who borrowed two or fewer books is 2 x 0 + 12 x 1 + 10 x 2 = 32.

These 32 books were borrowed by 2 + 12 + 10 = 24 students.

So we have 60 - 32 = 28 books left for the remaining 6 students. Since we want to maximize the number of books borrowed by a single student, we must minimize the number of books borrowed by the other 5 students. We see that if 5 of these students borrowed 3 books each, then we have 28 - 15 = 13 books for the last student.

Answer: D